A.K.H. Kwan

Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh

Abstract Concrete is a composite material with a variety of inhomogeneities. Its composite behavior may be studied analytically using the mesoscopic approach which treats the concrete as a three-phase system consisting of coarse aggregate, mortar matrix with fine aggregate dissolved in it, and interfacial zones between the coarse aggregate and the mortar matrix. For such mesoscopic study, it is first necessary to generate a random aggregate structure in which the shape, size and distribution of the aggregate particles resemble real concrete in the statistical sense. Then, if the composite structure is to be analyzed by the finite element method, a mesh for each of the three phases needs to be generated. In this paper, a procedure for generating random aggregate structures for rounded and angular aggregates based on the Monte Carlo random sampling principle is proposed and a method of mesh generation using the advancing front approach is developed. These are combined with a nonlinear finite element method for mesoscopic study of concrete whose methodology and results will be presented in part II of the paper.

Mesoscopic study of concrete II: nonlinear finite element analysis

Abstract At mesoscopic scale, concrete may be regarded as a three-phase composite consisting of coarse aggregate, mortar matrix and interfacial zones. Its composite behavior can be studied by generating a random aggregate structure which resembles the mesoscopic structure of concrete and analyzing the interaction between the three phases using the finite element method. A method of generating random aggregate structures taking into account the size, shape and spatial distributions of aggregate particles has been developed and presented in part I of the paper. Herein, a nonlinear finite element method suitable for mesoscopic study of concrete is developed. Goodman type interface elements are used to model the interfacial zones. Cracking and nonlinear constitutive properties of the materials are taken into account. A failure criterion combining tensile strength and fracture toughness is adopted. Stress relief as cracks propagate is also allowed for. An adaptive incremental displacement controlled iterative scheme which can deal with post–peak behavior is employed. The method is applied to study the strain localization of concrete under uniaxial tension in a numerical example.

Modeling dowel action of reinforcement bars for finite element analysis of concrete structures

Abstract A numerical model for the dowel action of reinforcement bars crossing cracks in concrete is developed for finite element analysis of concrete structures. The beam on elastic foundation theory is used to derive the dowel force–displacement relationship, which is expressed in a smeared form in terms of dowel stress and strain in order to be compatible with the smeared crack and smeared reinforcement models commonly used in finite element analysis. This dowel action model is incorporated in a finite element program that employs secant stiffness formulation and a displacement controlled iteration scheme for nonlinear analysis. Using the finite element program, the nonlinear behaviors of several reinforced concrete beams tested by others are analyzed well into the post-peak range. The beams are analyzed first with the dowel action neglected and then again with the dowel action incorporated. It is found that in certain cases, the dowel action can have significant effects on the shear strength and ductility of reinforced concrete beams and that the analytical results generally agree better with the experimental values when the dowel action is taken into account.

Local deformations and rotational degrees of freedom at beam-wall joints

Abstract Local deformations at beam-wall joints can significantly reduce the effective stiffness of coupling beams in shear/core wall structures. This phenomenon has been studied by many researchers and several methods of allowing for such effects have already been developed. However, in the existing methods, the beam-wall joint rotations are often mistaken as the rotations of the horizontal rigid arms leading to incompatibility between the beam and wall elements. Moreover, many practical difficulties with the actual applications of these methods have been encountered. In this paper, it is proposed that in order to resolve the problem of incompatibility between the beam and wall elements, the definition of the joint rotations should be changed to the rotations of the beam-wall interfaces. A new method of using joint elements to model the joint deformations, which can overcome the problems with the existing methods, is proposed and two alternative beam elements with joint deformations taken into account are developed. Finite element analysis is used to evaluate the local deformations and determine the joint element properties.

Effective stiffness of coupling beams connected to walls in out-of-plane directions

Abstract Based on recent studies on local deformations at coplanar and nonplanar beam–wall joints, the structural behavior of oblique beam–wall joints (joints at which the beams are at oblique angles to the walls) is analyzed and a joint element developed to model their behavior. Both in-plane and out-of-plane wall deformations at the beam–wall joints are taken into account. For general application to analysis of coupled shear/core walls, the stiffness matrix of oblique coupling beams (beams connected to walls at oblique angles) with local deformations at the joints allowed for, is derived. Using this stiffness matrix, the effective stiffness of coupling beams connected to walls in any direction is evaluated, and its dependence on the angles of connection studied. It is also shown through numerical examples that the coupling effect of oblique coupling beams can be quite substantial and thus, should not be neglected

Finite element analysis of effect of concrete confinement on behavior of shear walls

Abstract When concrete in the compression zone of a shear wall is confined by transverse reinforcement, both the strength and ductility of the wall would be increased. However, none of the existing analysis methods in the codes allows for such effect. Herein, a finite element model that takes into account the effect of concrete confinement is developed for nonlinear analysis of reinforced concrete structures. In this model, the confinement effect of the transverse reinforcement is incorporated by adjusting the compressive stress–strain relation of the concrete according to the confinement index proposed by Kappos. Shear wall models tested by others under constant vertical load and monotonically increasing horizontal load are analyzed and the analytical results for the failure modes and load–deflection curves of the walls are found to be in good agreement with the experimental results. Using the finite element model, a parametric study on the contribution of concrete confinement to the lateral resistance of shear walls is conducted. It is revealed that the effect of concrete confinement is more significant in walls with greater height to width ratio and/or subjected to larger axial compression load.

Equivalence of finite elements and analogous frame modules for shear/core wall analysis

Tall shear/core wall buildings may be analysed by the finite element method or the frame method. However, actual applications of these methods are not straightforward. For the finite element method, many lower order elements are found to be subjected to parasitic shear, which greatly stiffens the elements in their response to bending. On the other hand, the conventional frame method is afflicted by parasitic moment, which causes artificial flexure of the wall elements and thereby softens their response to shear. Various techniques, e.g. reduced integration, addition of bubble function and strain function formulation etc., have been used to eliminate parasitic shear, and several alternative analogous frame modules have been developed to overcome the parasitic moment problem. In this paper, it is shown that the various four-noded rectangular finite elements with parasitic shear removed and the analogous frame modules for dealing with parasitic moment are actually all equivalent to each other, though they look very different. Hence, the two separate methods are unified. Some important points on their applications are also discussed.

Rotational DOF in the frame method analysis of coupled shear/core wall structures

Abstract This study shows that the common practice in existing frame methods of assuming the rotations of the coupling beams at beam-wall joints to be equal to the rotations of the horizontal rigid arms would lead to incompatibility between the beam and wall elements at their joints and eventually errors in the effective stiffness of the coupling beams. It is postulated that to resolve the problem, the rotational DOF at the beam-wall joints should be changed to the rotations of the vertical fibres there. This would, however, necessitate the use of frame elements with two rotational DOF at each end or solid wall elements with rotational DOF at each node to model the structure. Such required frame and solid wall elements are developed in this paper based on a Timoshenko beam element with two rotational DOF at each end. The resulting new frame method is much more accurate and versatile than the existing frame methods.

Unification of existing frame analogies for coupled shear/core wall analysis

Abstract In order to overcome the artificial flexure problem with the conventional wide column frame analogy, several alternative frame analogies have been developed by Stafford Smith et al . and by Kwan. The framework modules developed by Stafford Smith et al . are incorporated with rotational d.o.f. for direct connection with the coupling beams, while the solid wall element developed by Kwan has no rotational d.o.f. In the present study, it is revealed that the framework modules should really be used only in their respective forms with no rotational d.o.f. and that the various framework modules are actually equivalent to each other. Comparing the stiffness matrix of the framework modules to that of Kwans solid wall element, it is further found that the framework modules are in fact also equivalent to Kwans solid wall element. Hence the various alternative frame analogies can be unified into one frame method and their characteristics as observed by different researchers can all be drawn together.

STATIC-DYNAMIC DISTRIBUTION FACTORS METHOD FOR TALL BUILDING ANALYSIS

Abstract A new approximate method of analysing three-dimensional tall building structures is presented. The method is a further development of the distribution factors method developed by Leung. It is proposed, based on the observation that the pattern of the out-of-plane displacement and rotation of the joints of a particular floor generally follows the shape of its own natural modes, to include the eigenvectors of the floor out-of-plane deflection as distribution factors in the analysis. By using both static and dynamic distribution factors to reduce the number of DOF, an efficient and yet sufficiently accurate analysis method is developed. Numerical examples demonstrate that in general the addition of only a few number of eigenvectors can significantly improve the accuracy of the results.